Time Delay Bias Research Articles

BDS pseudorange biases handling: Simultaneous estimation, daily magnitude and analytical comparison of the BDS PPP models

With the completed establishment of the Beidou global navigation satellite system (BDS-3), the BDS constellation is qualified for the global positioning, navigation and timing (PNT) services. The simultaneous observed B1I/B3I signals of the BDS-2 and BDS-3 satellites facilitate the BDS-2/BDS-3 joint precise point positioning (PPP) solution. For reasons related to the modulation modes, signal property, receiver front end design, precise satellite clock products arising from the different analysis centers and so on, BDS pseudorange biases are absorbed by the pseudorange measurements, including the pseudorange bias variation, signal distortion bias (SDB) and time delay bias (TDB). The large magnitude of the BDS pseudorange biases will degrade the BDS PPP performance. Herein, the simultaneous estimation of the BDS pseudorange biases are applied in BDS PPP and totally six pseudorange biases processing strategies are presented. The magnitudes of the existed BDS SDB and TDB are analyzed. The statistics showed that the BDS PPP performance in term of the convergence time and positioning accuracy can be remarkably improved by considering the BDS pseudorange biases. By comparing the BDS PPP performance in different scenarios, we recommend three processing schemes that are reducing weight of the BDS-2 pseudorange observations, estimating the BDS TDB as constant and neglecting the SDB, and estimating the BDS SDB as the constant per satellite. The analytical results can facilitate the optimal BDS PPP performance.

Modeling and performance assessment of BDS-2/BDS-3 triple-frequency ionosphere-free and uncombined precise point positioning

The global BeiDou Navigation Satellite System (BDS-3) and regional system (BDS-2) are transmitting signals on three or more frequencies, which brings more choices and practical potentials. To deeply integrate and fully utilize the BDS-2 and BDS-3 signals, this research is dedicated to the modeling and assessment of BDS-2/BDS-3 combined triple-frequency precise point positioning (PPP). Using ionosphere-free (IF) or uncombined (UC) observables, the three BDS-2/BDS-3 combined triple-frequency PPP models, named IF1213, IF123 and UC123 are developed. Particularly, new biases such as time delay bias (TDB) and inter-frequency bias (IFB) as well as the parameterizations are addressed. One-month observations from 16 Multi-GNSS Experiment (MGEX) stations located in and around the Asia-Pacific region are utilized to validate and compare the models. The results indicate that the three BDS-2/BDS-3 combined triple-frequency PPP models have the comparable performance and the third frequency makes a marginal contribution to positioning and tropospheric delay retrieval. The TDB should be carefully considered in BDS-2/BDS-3 combined PPP, especially for the IF123 model due to the larger absolute values of TDB. Meanwhile, the IFB derived from receiver uncalibrated code delay difference shows good stability in both short-term (intra-day) and long-term (inter-day) periods. In addition, demonstrated by triple-frequency PPP tests with one-month data from 47 global MGEX stations, the BDS-2/BDS-3 combined constellation allows for significantly improved convergence performance and positioning accuracy over the BDS-2-only constellation. The BDS-3 system has the ability to provide the precise positioning accuracy of 12.1/9.8/15.8 mm on a global scale after the convergence time of 23.0/13.2/24.7 min in east/north/up components.

Time delay bias between the second and third generation of BeiDou Navigation Satellite System and its effect on precise point positioning

To realize the deep integration of BeiDou-2 regional navigation satellite system (BDS-2) and BeiDou-3 global navigation satellite system (BDS-3), the time delay bias between BDS-2 and BDS-3 at the receiver side is analyzed for the joint BDS-2/BDS-3 precise point positioning (PPP). Twenty Multi-GNSS (Global Navigation Satellite System) Experiment tracking stations with different receiver types were selected to investigate the time-varying characteristics of time delay bias. We also make a comprehensive analysis about the influence of time delay bias on the ionosphere-free PPP and uncombined PPP. The results show that the daily mean values of time delay bias for consecutive days vary within 1 ns without apparent day-boundary discontinuities. In addition, the time delay bias for the receivers of the same brand can differ by several nanoseconds, especially for the TRIMBLE receivers. Without considering the time delay bias between BDS-2 and BDS-3, the pseudorange residuals, slant ionospheric delays, float ambiguities are subjected to change with the magnitude of the time delay bias, while the phase residuals and positioning accuracy are slightly affected. Moreover, the deviation of float ambiguity in ionosphere-free PPP caused by neglecting the time delay bias is larger than that of uncombined PPP.

PPP models and performances from single- to quad-frequency BDS observations

Nowadays, China BeiDou Navigation Satellite System (BDS) has been developed well and provided global services with highly precise positioning, navigation and timing (PNT) as well as unique short-message communication, particularly global system (BDS-3) with higher precision multi-frequency signals. The precise point positioning (PPP) can provide the precise position, receiver clock, and zenith tropospheric delay (ZTD) with a stand-alone receiver compared to the traditional double differenced relative positioning mode, which has been widely used in PNT, geodesy, meteorology and so on. However, it has a lot of challenges for multi-frequency BDS PPP with different strategies and more unknown parameters. In this paper, the detailed PPP models using the single-, dual-, triple-, and quad-frequency BDS observations are presented and evaluated. Firstly, BDS system and PPP method are introduced. Secondly, the stochastic models of time delay bias in BDS-2/BDS-3 PPP including the neglection, random constant, random walk and white noise are presented. Then, three single-frequency, four dual-frequency, four triple-frequency and four quad-frequency BDS PPP models are provided. Finally, the BDS PPP models progress and performances including theoretical comparison of the models, positioning performances, precise time and frequency transfer, ZTD, inter-frequency bias (IFB) and differential code bias (DCB) are presented and evaluated as well as future challenges. The results show that the multi-frequency BDS observations will greatly improve the PPP performances.

Accounting BDS3–BDS2 inter-system biases for precise time transfer

The rapid development of BDS not only brings opportunities but also new problems. This article has been verified that the biases exist between BDS-2 and BDS-3 precise point positioning time transfer. We defined internal biases of BDS as Time Delay Bias (TDB) for a distinguish with inter system biases (ISB) exists in different systems. Motivated by the bias, we make comprehensive analysis for determining the characteristics of TDB referring to all the receivers capable of BDS-2 along with BDS-3 signals, furtherly, three kinds of TDB stochastic model are designed for parameter estimation. Later, the influence on time transfer with different TDB estimation strategy is compared in the end. We have some findings: (1) It is confirmed that TDB indeed exists in JAVAD TRE_3, CETC-54-GMR-4016, GNSS GGR and UB4B0-13478 receivers. Without external frequency source, the characteristics of TDB is related to the receiver itself. With the same external frequency source, TDB tendency of two receivers show the same evolution. (2) It is concluded that the STD (Standard Deviation) and stability of TDB estimated with random walk model and constant model is superior to white noise model because of strong correlation among TDB time series. (3) It is verified that the stability of time transfer estimated as random walk model and constant model is smaller than that of white noise model, what is more, when the two sides were receivers of different brands, the significant deviation exists in the clock offset with TDB estimation and without TDB estimation. When the two sides are receiver of the same brand, marginal deviation exists in the clock offset with TDB estimation and without TDB estimation.

Improving BDS-2 and BDS-3 joint precise point positioning with time delay bias estimation

The third-generation BeiDou navigation satellite system (BDS-3) began providing a global positioning, navigation and timing (PNT) service on 27 December 2018. After completion of the construction of BDS-3, BDS-2 will continue to provide PNT services for the next few years. Hence, the technology of BDS-2/BDS-3 joint precise point positioning (PPP) has become very important. BDS-2 and BDS-3 are two generations of navigation systems, so a time delay bias may exist between them. To investigate the influence of time delay bias on BDS-2/BDS-3 joint PPP performance, four kinds of time delay bias processing strategies are performed, i.e. no operation, random constant, random walk process, and white noise process, with the datasets provided by the multi-GNSS experiment and the international GNSS monitoring and assessment system. The results demonstrate that the JAVAD TRE_3, CETC-54-GMR-4016 and GNSS_GGR receivers have obvious time delay bias between BDS-2 and BDS-3, whereas the UB4B0-13478 receiver has no obvious time delay bias. The positioning performances of the receivers with time delay bias in terms of positioning accuracy and convergence time can be improved when estimating the time delay bias parameters. It is recommended that the time delay bias is estimated as a random constant as it is the most effective of the four strategies. The positioning accuracy of BDS-2/BDS-3 PPP with time delay bias estimated as a random constant is improved by 2.38%, 9.71% and 6.74%, and the convergence time is reduced by 2.39%, 10.21% and 6.28%, respectively, compared with the no operation strategy in three coordinate components.

An analysis of nivolumab-mediated adverse events and association with clinical efficacy in resected stage III or IV melanoma (CheckMate 238).

9584 Background: In both previous 18- and 24-month follow-up reports from CheckMate 238, NIVO demonstrated significantly longer recurrence-free survival (RFS) than ipilimumab (IPI) in patients (pts) with resected stage IIIB/C or stage IV melanoma. Here we provide a more comprehensive analysis of treatment-related adverse events (TRAEs) for NIVO over discrete follow-up intervals and an investigation of the association of these AEs with efficacy (RFS). Methods: Eligible pts were aged ≥15 years and underwent complete resection of stage IIIB/C or IV melanoma. A total of 453 pts were treated with NIVO 3 mg/kg Q2W for up to 1 year. The primary endpoint was RFS. Pts were followed for safety for up to 100 days following their last dose; as of the previous 18-month database lock, all pts had been off study drug for > 100 days. Here safety data were analyzed within discrete time intervals: months 0–3 of treatment (0–3), months 3–12 of treatment (3–12), and from last dose to 100 days after last dose (+100). In addition, the association of TRAEs with RFS was investigated using the 24-month efficacy dataset, accounting for time-delay bias within the first 12 weeks after randomization. Results: The incidence of the first onset of TRAEs reported in ≥5% of pts was highest in the 0–3 time frame; the most common TRAEs with NIVO were fatigue (28% for 0–3 vs 6% for 3–12 vs 2% for +100), pruritus (16% vs 7% vs 1%), and diarrhea (15% vs 7% vs 2%). Most TRAEs with NIVO resolved within 3 months of occurrence, except for endocrine AEs, which could have required hormone supplementation, and skin AEs (median overall resolution time of 48 and 22 weeks, respectively). Similar results were observed in an analysis taking into account repeat occurrences of TRAEs over time. Analyses investigating the association of TRAEs with RFS are ongoing and will be presented. Conclusions: These results in pts with resected stage IIIB/C or IV melanoma are consistent with the established safety profile of NIVO. Based on the time periods analyzed, the majority of TRAEs with adjuvant NIVO occurred early during treatment, and patients had a reduced frequency of TRAEs after the treatment course. The majority of select TRAEs resolved within 3 months. Clinical trial information: NCT02388906.

Statistical framework for estimating GNSS bias

Abstract. We present a statistical framework for estimating global navigation satellite system (GNSS) non-ionospheric differential time delay bias. The biases are estimated by examining differences of measured line-integrated electron densities (total electron content: TEC) that are scaled to equivalent vertical integrated densities. The spatiotemporal variability, instrumentation-dependent errors, and errors due to inaccurate ionospheric altitude profile assumptions are modeled as structure functions. These structure functions determine how the TEC differences are weighted in the linear least-squares minimization procedure, which is used to produce the bias estimates. A method for automatic detection and removal of outlier measurements that do not fit into a model of receiver bias is also described. The same statistical framework can be used for a single receiver station, but it also scales to a large global network of receivers. In addition to the Global Positioning System (GPS), the method is also applicable to other dual-frequency GNSS systems, such as GLONASS (Globalnaya Navigazionnaya Sputnikovaya Sistema). The use of the framework is demonstrated in practice through several examples. A specific implementation of the methods presented here is used to compute GPS receiver biases for measurements in the MIT Haystack Madrigal distributed database system. Results of the new algorithm are compared with the current MIT Haystack Observatory MAPGPS (MIT Automated Processing of GPS) bias determination algorithm. The new method is found to produce estimates of receiver bias that have reduced day-to-day variability and more consistent coincident vertical TEC values.

Equilibrating errors: reliable estimation of information transmission rates in biological systems with spectral analysis-based methods

Shannon's seminal approach to estimating information capacity is widely used to quantify information processing by biological systems. However, the Shannon information theory, which is based on power spectrum estimation, necessarily contains two sources of error: time delay bias error and random error. These errors are particularly important for systems with relatively large time delay values and for responses of limited duration, as is often the case in experimental work. The window function type and size chosen, as well as the values of inherent delays cause changes in both the delay bias and random errors, with possibly strong effect on the estimates of system properties. Here, we investigated the properties of these errors using white-noise simulations and analysis of experimental photoreceptor responses to naturalistic and white-noise light contrasts. Photoreceptors were used from several insect species, each characterized by different visual performance, behavior, and ecology. We show that the effect of random error on the spectral estimates of photoreceptor performance (gain, coherence, signal-to-noise ratio, Shannon information rate) is opposite to that of the time delay bias error: the former overestimates information rate, while the latter underestimates it. We propose a new algorithm for reducing the impact of time delay bias error and random error, based on discovering, and then using that size of window, at which the absolute values of these errors are equal and opposite, thus cancelling each other, allowing minimally biased measurement of neural coding.

Resolution bias errors in spectral density, frequency response and coherence function measurements, IV: Time delay bias errors

The problem of time delay bias errors is treated in this part of the present series of papers as a special case of a general theory of resolution bias errors in spectral estimation presented in a previous part. It is shown that the main effect of an additional time delay between the output and the input of a physical system is to multiply the frequency response and coherence estimators which would be obtained without delay with the normalized autocorrelation function of the window function and its square respectively. Experimental results for the rectangular and Hanning windows are in accord with the theoretical predictions. The theoretical results given in the literature previously are valid for the rectangular window only but not for an arbitrary window function.

Time-delay bias errors in estimating frequency response and coherence functions from windowed samples of continuous and transient signals

An investigation is reported of the bias effect introduced by time delays when frequency response and coherence functions are estimated from windowed time samples. The magnitude of the bias error for both functions is shown to be dependent on both the nature of the data capture window and the amount of delay. The bias is found to be more severe for random data processed through a Hanning window than through a “boxcar” window. For transient signals that are fully captured through a boxcar window, the bias error is shown to be zero. Experimental investigation verifies the derived estimates for both boxcar and Hanning windows.

Coherence analysis applied to structural acoustic problems

This presentation discusses signal processing techniques and engineering requirements for solving structural acoustic multiple input/output problems using ordinary, partial, and multiple coherence functions. Practical matters are included on formulation of models, selection of input records, time delay bias errors, measurement interference effects, and statistical sampling errors. These topics are covered in the book by J. S. Bendat and A. G. Piersol [Engineering Applications of Correlation and Spectral Analysis (Wiley-Interscience, New York, 1980)]. Recent two-input/one-output models employing these methods are: (1) space shuttle tile problems where it is required to determine the response of tiles due to pressures from acoustic noise inputs over the tiles, versus that from correlated panel vibration inputs under the tiles (performed by A. G. Piersol); (2) a noise source identification problem where it is required to determine the relative contributions of a structure-borne noise input generated in an engine, versus a correlated cooling fan noise input from a fan mounted on the engine, to a farfield sound output (performed by W. G. Halvorsen).

Time delay bias errors in estimating frequency response and coherence functions

This paper discusses the problem of bias errors introduced when frequency response and coherence functions are estimated for systems in which a time delay is present. It is shown that a time delay between the input and output of a linear system causes the cross-spectral density to fluctuate as a function of frequency, where the period of fluctuation is dependent on the magnitude of the time delay. If the analysis bandwidth is not sufficiently small, or if frequency averaging is used to reduce the variance, the cross-spectral density estimate will have a negative bias. This error is transferred to estimates of the frequency response and coherence functions. Theory is developed showing the dependence of the bias errors on the time delay, the bandwidth and the length of the sample record of the input/output processes. Two experiments were designed to check the theory. In one experiment a loudspeaker, driven by white noise, and a microphone were used. The time delay was controlled by knowing the propagation time for acoustic waves between the loudspeaker and the microphone. In a second experiment a tape recorder was used with a fixed spacing between the record/playback heads to introduce a time delay. For both experiments comparison with theory was good.